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by diebeatsthegmat » Tue Apr 26, 2011 1:49 pm
D & E are two points on sides AB & AC of triangle ABC such that DE is parallel to BC. If the ratio of area of triangle ADE to that of the trapezium DECB is 25:144 and DE is 5 cm, then find the length of BC
a) 12 b) 13 c) 14 d) 11 e) 15

I KNOW THAT THE TRIANGLE ABC AND ADE ARE SIMILIAR AND I CAN FIND THE HEIGH OF ADE BUT I CANT FIND BC, CAN ANYBODY HELP PLEASE AND PLEASE TELL ME MORE ABOUT SIMILIAR TRIANGLE... I GOOGLED AND READ SOME BUT ITS SO VAGUE
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by Anurag@Gurome » Tue Apr 26, 2011 8:56 pm
diebeatsthegmat wrote:D & E are two points on sides AB & AC of triangle ABC such that DE is parallel to BC. If the ratio of area of triangle ADE to that of the trapezium DECB is 25:144 and DE is 5 cm, then find the length of BC
a) 12 b) 13 c) 14 d) 11 e) 15

I KNOW THAT THE TRIANGLE ABC AND ADE ARE SIMILIAR AND I CAN FIND THE HEIGH OF ADE BUT I CANT FIND BC, CAN ANYBODY HELP PLEASE AND PLEASE TELL ME MORE ABOUT SIMILIAR TRIANGLE... I GOOGLED AND READ SOME BUT ITS SO VAGUE
Image

ABC and ADE are similar triangles.
There is a theorem that states: The area of similar triangles are proportional to the squares of the corresponding sides.
Given that Area of ADE : Area of DECB = 25 : 144 implies Area of ADE : Area of ABC = 25 : (25 + 144) = 25 : 169
So, 25 : 169 = 5² : BC²
or BC² = 169 implies BC = 13

The correct answer is B.
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